In 2006, Warren Buffett pledged $30 billion to the Bill & Melinda Gates Foundation, challenging the Microsoft founder and his wife to improve the lives of impoverished people across the globe. Like any good investment manager, Buffett in December asked the couple for a progress ­report. This week, they gave their grateful response to Buffett — and a ­reminder that the world is getting better:

Dear Warren,

Ten years ago, when we first got word of your gift to the foundation, we were speechless. It was the biggest single gift anyone ever gave anybody for anything.

We knew we owed you a fantastic return on your investment.

Of course, philanthropy isn’t like business. We don’t have sales and profits to show you. There’s no share price to report. But there are numbers we watch closely to guide our work and measure our progress.

We’ll tell the story through the numbers that drive our work.

122 million — number of children’s lives saved since 1990

Melinda: Every September, the UN announces the number of children under 5 who died the previous year. Every year, this number breaks my heart and gives me hope. It’s tragic that so many children are dying, but every year more children live.

Bill: If you add up each year’s gains, 122 million children under age 5 have been saved over the past 25 years. These are children who would have died if mortality rates had stayed where they were in 1990.

Melinda: Saving children’s lives is an end in itself. But it has other benefits as well. If parents believe their children will survive — and they have access to contraceptives that let them time and space their pregnancies — they’re able to choose how many children to have.

Bill: When a mother can choose how many children to have, her children are healthier, they’re better nourished, their mental capacities are higher—and parents have more time and money to spend on each child’s health and schooling. That’s how families and countries get out of ­poverty.

86 percent — percentage of children worldwide who receive basic vaccines — the highest percentage in history

Melinda: Coverage for the basic package of childhood vaccines is the highest it’s ever been, at 86 percent. And the coverage gap between rich countries and developing countries is the lowest it’s ever been. This explains a lot of the gains in childhood survival — vaccines are the single biggest ­reason for the drop in ­under-5 deaths.

1 million — number of babies who die on the day they are born

Bill: The first day of life is especially dangerous for ­babies, and more than 2.5 million newborns die in their first month. The world hasn’t made as much progress in this area as we have in others. Newborn deaths now represent 45 percent of all childhood deaths, up from 40 percent in 1990.

Melinda: But some very poor countries have improved their survival rates by encouraging breastfeeding and increasing the number of trained health workers attending births. And health centers we’re funding in Africa are now doing autopsies so pathologists can learn more about the causes of newborn deaths . . . It’s super-­exciting to find countries that have figured things out. From 2008 through 2015, Rwanda, one of the poorest countries in Africa, cut its newborn mortality by 30 percent, down to 19 deaths per 1,000 births.

What were they doing in Rwanda? A few things so cheap that any government can support them: breastfeeding in the first hour and exclusively for the first six months. Cutting the umbilical cord in a hygienic way. And kangaroo care: skin-to-skin contact between mother and baby to raise the baby’s body temperature. These practices led to big drops in newborn deaths.

300 million — number of women in the developing world who use modern contraceptives

Melinda: In the developing world, 300 million women have access to modern contraceptives. This number is an all-time high, but there are still 225 million women in developing countries who want to use modern contraceptives and can’t get them. That’s tragic.

Contraceptives are one of the greatest antipoverty innovations in history. When women in developing countries space their births by at least three years, their children are almost twice as likely to reach their first birthday. When women can time and space their pregnancies, they are more likely to advance their education, earn an income and have healthy children. This leads to greater prosperity — and it starts with women who have the power to choose how many children to have.

75 million — number of women in ­self-help groups in India

Bill: Poverty is sexist. The poorer the society, the less power women have. Men ­decide if a woman is allowed to go outside, talk to other women, earn an income. The male dominance in poorer societies is mind-blowing.

Melinda: Fortunately, as a society becomes better off, a woman’s position in that society improves. But how do women in poor societies get more power now? Actually, women get more power from other women. About 75 million women are involved in self-help groups in India alone. The groups might form to help women get loans or share health practices, but once things get started, the women take it in the direction they want to go. That is empowerment.

1 percent — percentage of people surveyed who knew that extreme poverty had been cut in half since 1990

Bill: In a recent survey, just 1 percent knew that the world had cut extreme poverty in half, and 99 percent underestimated the progress. The survey wasn’t just testing knowledge, it was testing optimism, and the world didn’t score so well.

Melinda: Optimism isn’t just a belief that things will automatically get better; it’s a belief that we can make things better. And in many ways we are making the world better — global poverty is going down, childhood deaths are dropping, literacy is rising, the status of women and minorities around the world is improving.

Bill: One of my favorite books is Steven Pinker’s “The Better Angels of Our ­Nature.” It shows how violence has dropped dramatically over time. That’s startling news to people, because they tend to think things are not improving as much as they are. Actually, in significant ways, the world is a better place to live than it has ever been. Global poverty is going down, childhood deaths are dropping, literacy is rising, the status of women and ­minorities around the world is improving.

Warren, it won’t surprise you to know we’re more optimistic than ever.

Melinda: And more impatient too.

Bill: Especially for this:

Zero — the magic number

Bill: This is the number we’re striving toward every day at the foundation. Zero malaria. Zero HIV. Zero TB. Polio is closest to reaching that magic number. In 1988, there were 350,000 new cases of polio worldwide.

Last year, there were 37.

Melinda: Those cases were confined to Northern Nigeria and parts of Afghanistan and Pakistan. Immunizing children in conflict areas is hard — and dangerous. We’re in awe of the vaccinators who are taking risks to reach each child.

Bill: If things stay stable enough in the conflict areas, humanity could see its last case of polio sometime this year.

Warren, these numbers help capture the successes and struggles in global health. The problems are still here because they’re so hard to solve. But we have confidence in the world’s talent, energy and empathy — and that lets us end our letter with a bright look ahead.

Polio will soon be history. In our lifetimes, malaria will end. No one will die from AIDS. Few people will get TB. Children everywhere will be well nourished. And the death of a child in the ­developing world will be just as rare as the death of a child in the rich world.

We can’t put a date on these events, and we don’t know the sequence, but we’re confident of one thing: The future will ­surprise the pessimists.

Thank you for putting your trust in us, Warren. We won’t let you down.